Rates of Convergence of Recursively Defined Sequences

AbstractThis paper gives a generalization of a result by Matiyasevich which gives explicit rates of convergence for monotone recursively defined sequences. The generalization is motivated by recent developments in fixed point theory and the search for applications of proof mining to the field. It relaxes the requirement for monotonicity to the form xn+1⩽(1+an)xn+bn where the parameter sequences have to be bounded in sum, and also provides means to treat computational errors.The paper also gives an example result, an application of proof mining to fixed point theory, that can be achieved by the means discussed in the paper